Answer to Question #284683 in Physics for John

Question

At what temperature do Celsius and Fahrenheit are equivalent in value? Prove your answer.

Answer 1

Celsius and Fahrenheit are equivalent at -40 degrees (Celsius or Fahrenheit). Let's prove that. Let's first use the conversion formula from degrees Fahrenheit to degrees Celsius:

$$^{\circ}C=\dfrac{5}{9}(^{\circ}F-32),$$ $$x=\dfrac{5}{9}(x-32),$$ $$x-\dfrac{5}{9}x=-17.778,$$ $$0.444x=-17.778,$$ $$x=\dfrac{-17.778}{0.444}=-40\ degrees.$$

Let's use the conversion formula from degrees Celsius to degrees Fahrenheit:

$$^{\circ}F=(^{\circ}C\times\dfrac{9}{5})+32,$$ $$x=(x\times\dfrac{9}{5})+32$$ $$x-\dfrac{9}{5}x=32,$$ $$-0.8x=32,$$ $$x=\dfrac{32}{-0.8}=-40\ degrees.$$

Therefore, we prove that Celsius and Fahrenheit are equivalent at -40 degrees (Celsius or Fahrenheit).